Finite Group Databasebeta

← #356988

Subgroups — #356988

Order 512.

1772 conjugacy classes of subgroups.

The subgroup lattice has 941 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2367C211yesmaximal, characteristic
2C2×#1983C211yesmaximal, characteristic
3C2×#1958C211yesmaximal, characteristic
4C2×#1770C211yesmaximal, characteristic, complemented
5C2×#1763C211yesmaximal, characteristic, complemented
6C2×#1762C211yesmaximal, characteristic
7#13804C211yesmaximal, characteristic, complemented
8#10932C211yesmaximal, characteristic, complemented
9#10931C211yesmaximal, characteristic
10#10928C211yesmaximal, characteristic, complemented
11#10927C211yesmaximal, characteristic
12#10850C211yesmaximal, characteristic, complemented
13#10789C211yesmaximal, characteristic, complemented
14#10788C211yesmaximal, characteristic
15C4×#340C211yesmaximal, characteristic, complemented
16C22×#124C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#97C2211yescharacteristic
29C22×#97C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31#2367—24no—
32#2367C418yescomplemented
33C2×#391C2211yescharacteristic
34C2×#390C2211yescharacteristic
35C2×#388—21no—
36C2×#388—21no—
37C2×#385—21no—
38C2×#382C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C22⋊C4—21no—
45#1983C418yescomplemented
46#1958C418yescomplemented
47#1770—24no—
48#1763—24no—
49#1762—24no—
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1436—21no—
61#1436—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64#1434—21no—
65C4×#95—21no—
66C23×Q8C2311yescharacteristic
67C23×D4C2311yescharacteristic
68C24×C4—21no—
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C2×#124—22no—
74C2×#124—22no—
75C2×#124—22no—
76C2×#124C2×C414yes—
77C2×#124C2×C414yes—
78C2×#124C2×C414yes—
79C2×C4×Q8—22no—
80C2×C4×Q8—22no—
81C2×C4×Q8—22no—
82C2×C4×Q8—41no—
83C2×C4×Q8—41no—
84C2×C4×Q8C2×C414yes—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—22no—
88C2×C4×D4—41no—
89C2×C4×D4—41no—
90C2×C4×D4C2×C414yes—
91C22×C4⋊C4—21no—
92C22×C4⋊C4D411yescharacteristic
93C22×C4⋊C4D411yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C42—21no—
106C22×C42—21no—
107C22×C42—21no—
108C22×C42—21no—
109C22×C42—21no—
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113C2×C4⋊C8—22no—
114C2×C4⋊C8—22no—
115C2×C4⋊C8C2×C414yescomplemented
116C2×#103—22no—
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—22no—
120C2×#103—41no—
121C2×#103—41no—
122C2×#103—41no—
123C2×#103—41no—
124C2×#103C2×C414yescomplemented
125C2×#103C2×C414yescomplemented
126C2×#103C2×C414yescomplemented
127C2×#103C2×C414yescomplemented
128C2×#102—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#102—22no—
132C2×#102—41no—
133C2×#102—41no—
134C2×#102—41no—
135C2×#102—41no—
136C2×#102C2×C414yes—
137C2×#102C2×C414yes—
138C2×#102C2×C414yes—
139C2×#102C2×C414yes—
140C2×#97—22no—
141C2×#97—22no—
142C2×#97—22no—
143C2×#97—22no—
144C2×#97—41no—
145C2×#97—41no—
146C2×C4×C8—22no—
147C2×C4×C8—22no—
148C2×C4×C8C2×C414yescomplemented
149#391—22no—
150#391C2×C414yes—
151#390—22no—
152#390C2×C414yes—
153#388—28no—
154#388—28no—
155#385—28no—
156#382—22no—
157#382C2×C414yescomplemented
158C4×C4⋊C4—22no—
159C4×C4⋊C4—22no—
160C4×C4⋊C4—22no—
161C4×C4⋊C4—22no—
162C4×C4⋊C4—41no—
163C4×C4⋊C4—41no—
164C4×C4⋊C4C2×C414yes—
165C4×C4⋊C4C2×C414yes—
166C4×C4⋊C4C2×C414yescomplemented
167C4×C4⋊C4D414yes—
168C4×C22⋊C4—28no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177C2×#95—21no—
178C2×#95—21no—
179C2×#95—21no—
180C2×#95—21no—
181C2×#95D411yescharacteristic
182C2×#95D411yescharacteristic
183#340—22no—
184#340—22no—
185#340—22no—
186#340—22no—
187#340—22no—
188#340—41no—
189#340—41no—
190#340D414yes—
191#336—22no—
192#336—22no—
193C25—21no—
194C22×Q8—21no—
195C22×Q8—21no—
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8C22×C412yes—
206C22×Q8C22×C412yes—
207C22×Q8C22×C412yes—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—21no—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4C22×C412yes—
220C22×D4C22×C412yes—
221C22×D4C22×C412yes—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—24no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—81no—
235C23×C4—81no—
236C23×C4C2×D411yescharacteristic
237C23×C4C2×D411yescharacteristic
238C23×C4C2×D411yescharacteristic
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2411yescharacteristic
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8C22×C412yes—
266C22×C8C22×C412yes—
267C22×C8C22×C412yes—
268C22×C8C22×C412yes—
269C22×C8C2×D412yes—
270C22×C8#4112yes—
271#124—28no—
272#124—28no—
273#124—28no—
274#124C42116yescomplemented
275C4×Q8—28no—
276C4×Q8—44no—
277C4×Q8—44no—
278C4×Q8—44no—
279C4×D4—28no—
280C4×D4—44no—
281C4×D4—44no—
282C4×D4—44no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4C22⋊C414yes—
317C2×C4⋊C4C22⋊C414yes—
318C2×C4⋊C4C22×C412yes—
319C2×C4⋊C4C22×C412yes—
320C2×C4⋊C4C22×C412yes—
321C2×C4⋊C4C22×C412yes—
322C2×C4⋊C4C22×C412yes—
323C2×C4⋊C4C22×C412yes—
324C2×C4⋊C4C2×D412yes—
325C2×C4⋊C4C2×D412yes—
326C2×C4⋊C4#4112yes—
327C2×C4⋊C4#4112yes—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—81no—
342C2×C22⋊C4—81no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—42no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42—42no—
360C2×C42—81no—
361C2×C42—81no—
362C2×C42—81no—
363C2×C42—81no—
364C2×C42—81no—
365C2×C42—81no—
366C2×C42C22×C412yes—
367C2×C42C22×C412yes—
368C2×C42C22×C412yes—
369C2×C42C22×C412yes—
370C2×C42C22×C412yes—
371C2×C42C2×D412yes—
372C2×C42C2×D412yes—
373C2×C42C2×D412yes—
374C2×C42#4112yes—
375C2×C42#4112yes—
376C4⋊C8—28no—
377#103—28no—
378#103—28no—
379#103—44no—
380#103—44no—
381#102—28no—
382#102—28no—
383#102—44no—
384#102—44no—
385#97—44no—
386#97—44no—
387C4×C8—28no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—81no—
399#95—81no—
400#95C22⋊C414yes—
401#95C22⋊C414yes—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24—41no—
412C24—41no—
413C24—41no—
414C24—41no—
415C24—41no—
416C24—41no—
417C24C22×D411yescharacteristic
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8—41no—
445C2×Q8C2×C4214yes—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4C2×C4214yes—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—84no—
558C22×C4—84no—
559C22×C4—84no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4C2×C22⋊C412yes—
563C22×C4C2×C22⋊C412yes—
564C22×C4C2×C22⋊C412yes—
565C22×C4C2×C22⋊C412yes—
566C22×C4C2×C22⋊C412yes—
567C22×C4C2×C22⋊C412yes—
568C22×C4C4×D412yes—
569C22×C4C4×D412yes—
570C22×C4C4×D412yes—
571C22×C4C4×D412yes—
572C22×C4C23×C411yescharacteristic
573C22×C4C23×C411yescharacteristic
574C22×C4C23×C411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C2×#4111yescharacteristic
578C22×C4C2×#4111yescharacteristic
579C22×C4C2×#4111yescharacteristic
580C22×C4C2×#4111yescharacteristic
581C22×C4C2×#4111yescharacteristic
582C22×C4H(5,𝔽2)11yescharacteristic
583C22×C4H(5,𝔽2)11yescharacteristic
584C22×C4H(5,𝔽2)11yescharacteristic
585C22×C42−1+411yescharacteristic
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8C4×D414yes—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—48no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4C4×D414yes—
640C4⋊C4C4×D414yes—
641C22⋊C4—216no—
642C22⋊C4—216no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—84no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—48no—
655C42—84no—
656C42—84no—
657C42—84no—
658C42—84no—
659C42C2×C4214yes—
660C42#11714yes—
661C42C4×D414yes—
662C42C4×D414yes—
663C23—24no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—81no—
683C23—81no—
684C23—81no—
685C23—81no—
686C23—81no—
687C23—81no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23—81no—
692C23—81no—
693C23—81no—
694C23—81no—
695C23—81no—
696C23—81no—
697C23—81no—
698C23C22×C22⋊C411yescharacteristic
699C23C2×C4×D411yescharacteristic
700C23C2×C4×D411yescharacteristic
701C23D4211yescharacteristic
702C23#54611yescharacteristic
703C23#54811yescharacteristic
704C23#55011yescharacteristic
705C23#57511yescharacteristic
706C23#57511yescharacteristic
707C23#57511yescharacteristic
708C23#57511yescharacteristic
709C23#57611yescharacteristic
710C23#57711yescharacteristic
711C23#57711yescharacteristic
712C23#57811yescharacteristic
713Q8—24no—
714Q8—24no—
715Q8—42no—
716Q8—42no—
717Q8—42no—
718Q8—42no—
719Q8—42no—
720Q8—42no—
721D4—24no—
722D4—24no—
723D4—42no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—816no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4C4×C22⋊C414yes—
820C2×C4C4×C22⋊C414yes—
821C2×C4C22×C4211yescharacteristic
822C2×C4C2×#11711yescharacteristic
823C2×C4C2×C4×D411yescharacteristic
824C2×C4C2×C4×D411yescharacteristic
825C2×C4C2×C4×D411yescharacteristic
826C2×C4C2×C4×D411yescharacteristic
827C2×C4C2×C4×D411yescharacteristic
828C2×C4C4×#4111yescharacteristic
829C2×C4C4×#4111yescharacteristic
830C2×C4C4×#4111yescharacteristic
831C2×C4#51811yescharacteristic
832C2×C4#51811yescharacteristic
833C2×C4#51811yescharacteristic
834C2×C4#52011yescharacteristic
835C2×C4#52011yescharacteristic
836C2×C4#52011yescharacteristic
837C2×C4D4211yescharacteristic
838C2×C4#54611yescharacteristic
839C2×C4#54711yescharacteristic
840C2×C4#54811yescharacteristic
841C2×C4#55011yescharacteristic
842C2×C4#55011yescharacteristic
843C2×C4#55311yescharacteristic
844C2×C4#55311yescharacteristic
845C2×C4#55511yescharacteristic
846C2×C4#55611yescharacteristic
847C2×C4#55911yescharacteristic
848C2×C4#55911yescharacteristic
849C8—24no—
850C8—42no—
851C8—42no—
852C8—42no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22C2×C4×C22⋊C411yescharacteristic
869C22D4×C22⋊C411yescharacteristic
870C22#234111yescharacteristic
871C22#236111yescharacteristic
872C22#236311yescharacteristic
873C22#236611yescharacteristic
874C22#236711yescharacteristic
875C22#289611yescharacteristic
876C22#289611yescharacteristic
877C22#289711yescharacteristic
878C22#289811yescharacteristic
879C22#294311yescharacteristic
880C22#294311yescharacteristic
881C22#294311yescharacteristic
882C22#294311yescharacteristic
883C22#294611yescharacteristic
884C22#294711yescharacteristic
885C22#295111yescharacteristic
886C22#295211yescharacteristic
887C22#327311yescharacteristic
888C22#327511yescharacteristic
889C22#327511yescharacteristic
890C22#327711yescharacteristic
891C22#332211yescharacteristic
892C22#332311yescharacteristic
893C22#332611yescharacteristic
894C22#332711yescharacteristic
895C22#337011yescharacteristic
896C22#337111yescharacteristic
897C22#337611yescharacteristic
898C22#337711yescharacteristic
899C22#340111yescharacteristic
900C22#340111yescharacteristic
901C22#340211yescharacteristic
902C22#340311yescharacteristic
903C4—24no—
904C4—24no—
905C4—42no—
906C4—42no—
907C4—44no—
908C4—42no—
909C4—42no—
910C4—44no—
911C4—44no—
912C4—82no—
913C4—82no—
914C4—82no—
915C4—82no—
916C4C42×D411yescharacteristic
917C4#227511yescharacteristic
918C4#235411yescharacteristic
919C4#235711yescharacteristic
920C4#236111yescharacteristic
921C4#236311yescharacteristic
922C4#236611yescharacteristic
923C4#236711yescharacteristic
924C2—84no—
925C2#1382011yescharacteristic
926C2#2041111yescharacteristic
927C2#2041511yescharacteristic
928C2#2242711yescharacteristic
929C2#2242911yescharacteristic
930C2#2254811yescharacteristic
931C2#2254911yescharacteristic
932C2#2300511yescharacteristic
933C2#2300611yescharacteristic
934C2#2310311yescharacteristic
935C2#2310411yescharacteristic
936C2#2318911yescharacteristic
937C2#2319111yescharacteristic
938C2#2322411yescharacteristic
939C2#2322511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×#1770C2semidirect
5. C2×#1763C2semidirect
7. #13804C2semidirect
8. #10932C2semidirect
10. #10928C2semidirect
12. #10850C2semidirect
13. #10789C2semidirect
15. C4×#340C2semidirect
32. #2367C4semidirect
45. #1983C4semidirect
46. #1958C4semidirect
115. C2×C4⋊C8C2×C4semidirect
124. C2×#103C2×C4semidirect
125. C2×#103C2×C4semidirect
126. C2×#103C2×C4semidirect
127. C2×#103C2×C4semidirect
148. C2×C4×C8C2×C4semidirect
157. #382C2×C4semidirect
166. C4×C4⋊C4C2×C4semidirect
274. #124C42semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#23672
C2×#19832
C2×#19582
C2×#17702
C2×#17632
C2×#17622
#138042
#109322
#109312
#109282
#109272
#108502
#107892
#107882
C4×#3402